PSO模型种群多样性与学习参数的关系研究

摘要

PSO can easily suffer from the premature convergence when solving complex mulfimodal problems. It is an important method for relieving the premature convergence to control the population diversity by adjusting the inertia weight and acceleration coefficients. However, the setting of the inertia weight and acceleration coefficients is dependent on the design of experiments and lack of the support of the theory. To solve this problem, the new method is proposed in which the change of the prospective population diversity is used to adjust the setting of learning parameters in this paper. Firstly, the expression of the population diversity at the next time step is computed in the condition of the known current population state. Then the mathematic relationship between the inertia weight, acceleration coefficients and the population diversity at the next time step is presented by the extremum theory on multivariate function, which provides a theoretical foundation to control the population diversity by learning parameters.%粒子群优化(Particle Swarm Optimzation,PSO)算法在求解复杂多峰问题时,易陷入早期收敛.通过调整惯性权重和加速系数来控制种群多样性是缓解PSO早期收敛的一个重要手段,但是目前对惯性权重和加速系数的设置主要依赖于实验设计,缺乏必要的理论支撑.针对该问题,本文提出了一种以种群未来的多样性变化调整PSO算法参数的方法.该方法首先在种群当前状态已知的条件下计算种群下一时刻多样性的期望表达式,再采用多元函数极值理论的分析方法给出了惯性权重,加速系数与种群下一时刻多样性的数学关系,该结果为PSO学习参数控制种群多样性提供有力的数学理论依据.